How can I copy one side of a rig to the other?
In order to mirror a rig down the very middle, you'll need the 3d cursor reset (ShiftC) and used as your 'Pivot Point' (.). That'll determine the mirror center, so long as the rig itself is placed correctly in the center (0,0,0). Now Select any half of the armature (excluding the spine/middle) and duplicate it with ShiftD, next press CtrlM + (the axis you are working along, usually  X) to mirror it over to the other side. With the selection still instact, press W > Flip Names to update the names so something like upper-arm.L becomes upper-arm.R. 

After doing this, the mirrored bones might have a different roll from the other side. To fix, select the original bones (can just invert selection with CtrlI if you still have the mirrored side selected), enable X-Axis mirror under Armature Options in the toolshelf and press CtrlR to fix the roll.